Find the slant asymptote, if any, of the graph of the rational function.
-$$h ( x ) = \frac { x ^ { 3 } + 9 } { x ^ { 2 } + 7 x }$$
A) $y = x - 7$
B) $y = x + 7$
C) $y = x + 9$
D) $y = x$

Question

Quizplus · Accepted Answer

To find the slant (oblique) asymptote of the given rational function, we divide the numerator by the denominator. The division $ \frac { x ^ { 3 } + 9 } { x ^ { 2 } + 7 x }$ simplifies to $x - 7 + \frac{9}{x^2 + 7x}$. The quotient $x - 7$ represents the slant asymptote, as the remainder becomes insignificant for large values of $x$.

Find the Slant Asymptote, If Any, of the Graph of the Rational